need help with , five hundred raffle tickets are sold for $3.00 each, one prize of $500.00 is to be awarded, Raul purchased one ticket.
a)his expected value is
b)the fair price of the ticket
To find the expected value and fair price of the ticket, we need to understand a few key concepts. The expected value is calculated by multiplying each outcome by its probability and summing them up, while the fair price represents the maximum amount someone should be willing to pay for the ticket. Let's break it down step by step:
a) Expected Value:
1. Calculate the probability of winning: Since there is only one prize and 500 tickets sold, the probability of winning is 1/500.
2. Calculate the value of winning: The prize is $500.
3. Multiply the probability by the value of winning: (1/500) * $500 = $1.
Therefore, the expected value for Raul is $1. This means if Raul repeatedly played this raffle many times, he would ultimately expect to win $1 on average per ticket.
b) Fair Price:
To determine the fair price, we need to determine how much each ticket is worth on average. If someone's expected value is greater than the price they are paying for the ticket, it might be a good deal.
1. Calculate the average cost of a ticket: Divide the total cost of all tickets sold by the number of tickets. In this case, $3.00 * 500 = $1500. Then, divide $1500 by the number of tickets (500) to get the average cost per ticket: $1500 / 500 = $3.00.
2. Compare the average cost per ticket to the expected value. The fair price is the maximum amount someone should pay. If it is higher than the average cost per ticket, it would not be fair. In this case, the expected value (calculated in part a) is $1. Since $1 is less than $3, the fair price of the ticket is $3.00 or less.
Therefore, based on the calculations, the expected value for Raul is $1, and the fair price of the ticket is $3.00.